Markowitz'in ortalama-varyans portföy optimizasyon modeli için metasezgisel yöntemlerin değerlendirilmesi ve karşılaştırılması

Öz

Portföy seçimi, tatmin edici bir yatırım getirisi elde etmek için birden fazla varlık içeren portföyler arasından bir varlık kombinasyonu seçme sürecidir. Markowitz (1952) tarafından önerilen ortalama varyans modeli, portföy seçim problemi için yaygın olarak kullanılmaktadır. Portföydeki varlıkları minimum risk ve maksimum getiriye dayalı olarak seçen bir karesel programlama modelidir. Karesel programlama probleminin çözümü için genellikle klasik optimizasyon algoritmaları kullanılmaktadır. Son yıllarda, portföy seçim problemlerinin çözümü için klasik optimizasyon tekniklerine ek olarak metasezgisel optimizasyon algoritmaları kullanılmaktadır. Metasezgisel yöntemler, kesin çözüm yöntemleri ile makul bir sürede çözülemeyen karmaşık optimizasyon problemlerini çözmek için tasarlanmış algoritmalardır. Farklı alanlar için çeşitli metasezgisel algoritmalar geliştirilmektedir. Bu çalışmada Aralık 2016 - Aralık 2017 tarihleri arasında BİST30 endeksinde işlem gören 30 hisse senedinin günlük kapanış fiyatlarından elde edilen veri seti kullanılmıştır. Optimal portföy oluşturmak için Markowitz'in ortalama varyans modeli ele alınmıştır. Optimal portföyü belirlemek için çoğunlukla metasezgisel yöntemlerden, Parçacık Sürüsü Optimizasyonu ve Diferansiyel Evrim ve Yapay Arı Kolonisi uygulanmıştır. Bu yöntemlerin performansları, risk değerleri yani portföy varyansları dikkate alınarak karşılaştırılmıştır.

Anahtar Kelimeler

• Yapay arı kolonisi
• Diferansiyel evrim
• Metasezgiseller
• Parçacık Sürü Optimizasyonu
• Portföy optimizasyonu
• Karesel programlama

Evaluation and comparison of metaheuristic methods for Markowitz’s mean-variance portfolio optimization model

Öz

 Portfolio selection is the process of selecting a combination of assets among portfolios containing multiple assets to achieve a satisfactory return on investment. Mean-variance model proposed by Markowitz (1952) has been extensively used for portfolio selection problem. It is a quadratic programming model based on the minimum risk and maximum return by choosing assets in the portfolio. Generally, classical optimization algorithms have been used for solving the quadratic programming problem. Recently, metaheuristic optimization algorithms have been used in addition to classical optimization techniques for solving portfolio selection problems. Metaheuristic methods are designed to solve complex optimization problems that cannot be solved in a reasonable time with the definitive solution methods. Various metaheuristic methods have been developed for different areas. In this study, BIST30 index data set obtained from daily closing prices of 30 stocks between December 2016 - December 2017 was used. Markowitz’s mean-variance model is considered to constitute an optimal portfolio. , Particle Swarm Optimization, Differential Evolution, and Artificial Bee Colony which are mostly used metaheuristic methods, are applied to determine an optimal portfolio. Performances of these methods are compared by considering risk values, i.e. portfolio variances.  

Anahtar Kelimeler

• Artificial Bee Colony
• Differential Evolution
• Metaheuristics
• Particle Swarm Optimization
• Portfolio Optimization
• Quadratic programming

Kaynakça

1. [1] H. Markowitz, 1952, Portfolio selection, The Journal of Finance, 7 (1), 77-91.
2. [2] Y. Crama, M. Schyns, 2003, Simulated Annealing for complex portfolio selection problems, European Journal of Operational Research, 150 (3), 546-571.
3. [3] K. Doerner, W. J. Gutjahr, R. F. Hartl, C. Strauss, C. Stummer, 2004, Pareto Ant Colony Optimization: A metaheuristic approach to multiobjective portfolio selection, Annals of Operations Research, 131 (1-4), 79-99.
4. [4] M. Ehrgott, X. Gandibleux, 2004, Approximative solution methods for multiobjective combinatorial optimization, Sociedad de Estadistica e Investigacidn Operutiva, 12 (1), 1-89.
5. [5] T. Cura, 2009, Particle swarm optimization approach to portfolio optimization, Nonlinear Analysis: Real World Applications, 10 (4), 2396-2406
6. [6] H. R. Golmakani, M. Fazel, 2011, Constrained portfolio selection using Particle Swarm Optimization, Expert Systems with Applications, 38 (7), 8327-8335.
7. [7] H. Zhu, Y. Wang, K. Wang, Y. Chen, 2011, Particle Swarm Optimization for the constrained portfolio optimization problem, Expert Systems with Applications, 38 (8), 10161-10169.
8. [8] G.-F. Deng, W.-T. Lin, C.-C. Lo, 2012, Markowitz-based portfolio selection with cardinality constraints using improved Particle Swarm Optimization, Expert Systems with Applications, 39 (4), 4558-4566.

9. [9] K. Lwin, R. Qu, 2013, A hybrid algorithm for constrained portfolio selection problems, Applied Intelligence, 39 (2), 251-266.
10. [10] A. Z. Çelenli, E. Eğrioğlu, B. Ş. Çorba, 2015, İMKB 30 endeksini oluşturan hisse senetleri için Parçacık Sürü Optimizasyonu yöntemlerine dayalı portföy optimizasyonu, Doğuş Üniversitesi Dergisi, 16 (1), 25-33.
11. [11] H. Akyer, C.B. Kalayci, H. Aygören, 2018, Ortalama-varyans portföy optimizasyonu için Parçacık Sürü Optimizasyonu algoritması: Bir Borsa İstanbul uygulaması, Pamukkale University Journal of Engineering Sciences, 24 (1), 124-129.
12. [12] J. Doering, R. Kizys, A.A. Juan, À. Fitó, O. Polat, 2019, Metaheuristics for rich portfolio optimisation and risk management: Current state and future trends, Operations Research Perspectives, 6,100121.
13. [13] C.B. Kalayci, O. Ertenlice, M.A. Akbay, 2019, A comprehensive review of deterministic models and applications for mean-variance portfolio optimization, Expert Systems with Applications, 125, 345–368.
14. [14] C.B. Kalaycı, O. Polat, M.A. Akbay, 2020, An efficient hybrid metaheuristic algorithm for cardinality constrained portfolio optimization, Swarm and Evolutionary Computation, 54, 100662, 1-16.
15. [15] M. Corazza, G. di Tollo, G. Fasano, R. Pesenti, 2021, A novel hybrid PSO-based metaheuristic for costly portfolio selection problems, Annals of Operations Research, 304,109–137.
16. [16] E-G. Talbi, 2009, Metaheuristics: From design to implementation, John Wiley & Sons Inc.
17. [17] X.-S. Yang, 2010, Engineering optimization an introduction with metaheuristic applications, John Wiley & Sons Inc., New Jersey.
18. [18] S. Kirkpatrick, C. D. Gelatt, M. P.Vecchi, 1983, Optimization by Simulated Annealing, Science, 220 (4598), 671–680.
19. [19] B. Abbasi, A.H.E. Jahromi, J. Arkat, M. Hosseinkouchack, 2006, Estimating the parameters of Weibull distribution using Simulated Annealing Algorithm, Applied Mathematics and Computation, 183 (1), 85-93.
20. [20] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, 1953 Equation of state calculations by fast computing machines, The Journal of Chemical Physics, 21,1087–1092.
21. [21] V. Cerny, 1985, Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm, Journal of Optimization Theory and Applications, 45, 41–51.
22. [22] İ. Boussaïd, J. Lepagnot, P. Siarry, 2013, A survey on optimization metaheuristics, Information Sciences, 237, 82–117
23. [23] D.S. Johnson, C. R. Aragon, L.A. McGeoch, C. Chevon, 1989, Optimization by Simulated Annealing: An experimental evaluation; Part 1, Graph Partitioning, Operations Research, 37 (6), 865-892.
24. [24] C. C. Ribeiro, S.L. Martins, I. Rosetti, 2007, Metaheuristics for optimization problems in computer communication, Computer Communications, 30, 656-669.
25. [25] J. Kennedy, R. C. Eberhart, 1995, Particle Swarm Optimization, IEEE International Conference on Neural Networks, Perth, Australia, 1942–1948.
26. [26] J. Kennedy, R. C. Eberhart, 2001, Swarm Intelligence. Morgan Kaufmann, San Francisco, CA,
27. [27] Y. Shi, R. Eberhart, 1998, A modified Particle Swarm Optimizer, Proceedings of IEEE World congress on computational intelligence. The 1998 I.E. international conference on evolutionary computation, 69–73.
28. [28] S.S. Rao, 2009, Engineering optimization: Theory and practice, John Wiley&Sons.
29. [29] H.H. Örkcü, V.S. Özsoy, E. Aksoy, M. İ. Doğan, 2015b, Estimating the parameters of 3-p Weibull distribution using Particle Swarm Optimization: A comprehensive experimental comparison, Applied Mathematics and Computation, 268, 201–226.
30. [30] Ş. Acıtaş, Ç.H. Aladağ, B. Şenoğlu, 2019, A new approach for estimating the parameters of Weibull distribution via particle swarm optimization: An application to the strengths of glass fibre data, Reliability Engineering&System Safety, 183, 116–127.
31. [31] R. Storn, 1996, On the usage of Differential Evolution for function optimization, Fuzzy Inf. Process. Soc. 1996. NAFIPS., 1996 Bienn. Conf. North Am., IEEE, 519–523.
32. [32] R. Storn, K. Price, 1997, Differential Evolution–a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11, 341–359.
33. [33] K. Price, R.M. Storn, J.A. Lampinen, 2006, Differential Evolution: a practical approach to global optimization, Springer Science & Business Media.
34. [34] L. Gui, X. Xia, F. Yu, H. Wu, R. Wu, B. Wei, Y. Zhang, X. Li, G. He, 2019, A multi-role based Differential Evolution, Swarm and Evolutionary Computation, 50, 100508.
35. [35] H.H. Örkcü, E. Aksoy, M. İ. Doğan, 2015a, Estimating the parameters of 3-p Weibull distribution through Differential Evolution, Applied Mathematics and Computation, 251, 211–224.
36. [36] S. Das, S.S. Mullick, P.N. Suganthan, 2016, Recent advances in Differential Evolution–an updated survey, Swarm and Evolutionary Computation, 27, 1–30.
37. [37] D. Karaboğa, 2005, An idea based on honey bee swarm for numerical optimization, Technical Report-tr06, Erciyes University, Engineering Faculty, Computer Engineering Department.
38. [38] B. Akay, D. Karaboğa, , 2012, A modified Artificial Bee Colony Algorithm for real-parameter optimization, Information Sciences, 192, 120-142.
39. [39] A. Rajasekhar, S. Lynn, S. Das, P.N. Suganthan, 2017, Computing with the collective intelligence of honey bees–a survey, Swarm and Evolutionary Computation, 32, 25–48.
40. [40] D. Karaboğa, C. Öztürk, 2011, A novel clustering approach: Artificial Bee Colony (ABC) algorithm, Applied Soft Computing, 11, 652–657.
41. [41] H. Konno, H. Yamazaki, 1991, Mean-absolute deviation portfolio optimization model and its applications to Tokyo Stock Market, Management Science, 37 (5), 519-531.
42. [42] C. D. Feinstein, M. N. Thapa, 1993, A reformulation of a mean-absolute deviation portfolio optimization model, Management Science, 39 (12), 1552-1554.
43. [43] Ö. Türkşen, M. Tez, (2016). An Application of Nelder-Mead Heuristic-based Hybrid Algorithms: Estimation of Compartment Model Parameters. International Journal of Artificial Intelligence, 14(1), 112-129.”